Basic properties
| Modulus: | \(4275\) | |
| Conductor: | \(4275\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4275.he
\(\chi_{4275}(13,\cdot)\) \(\chi_{4275}(52,\cdot)\) \(\chi_{4275}(67,\cdot)\) \(\chi_{4275}(97,\cdot)\) \(\chi_{4275}(148,\cdot)\) \(\chi_{4275}(223,\cdot)\) \(\chi_{4275}(238,\cdot)\) \(\chi_{4275}(592,\cdot)\) \(\chi_{4275}(697,\cdot)\) \(\chi_{4275}(763,\cdot)\) \(\chi_{4275}(922,\cdot)\) \(\chi_{4275}(952,\cdot)\) \(\chi_{4275}(1003,\cdot)\) \(\chi_{4275}(1078,\cdot)\) \(\chi_{4275}(1123,\cdot)\) \(\chi_{4275}(1447,\cdot)\) \(\chi_{4275}(1552,\cdot)\) \(\chi_{4275}(1687,\cdot)\) \(\chi_{4275}(1723,\cdot)\) \(\chi_{4275}(1762,\cdot)\) \(\chi_{4275}(1777,\cdot)\) \(\chi_{4275}(1858,\cdot)\) \(\chi_{4275}(1933,\cdot)\) \(\chi_{4275}(1948,\cdot)\) \(\chi_{4275}(1978,\cdot)\) \(\chi_{4275}(2302,\cdot)\) \(\chi_{4275}(2473,\cdot)\) \(\chi_{4275}(2542,\cdot)\) \(\chi_{4275}(2578,\cdot)\) \(\chi_{4275}(2617,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1901,1027,1351)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{11}{20}\right),e\left(\frac{11}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 4275 }(148, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{180}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(-i\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{31}{180}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{47}{180}\right)\) | \(e\left(\frac{173}{180}\right)\) |